Question

Two blocks of masses 10 kg and 30 kg are placed along a vertical line. The first block is raised through a height of 7 cm. By what distance should the second mass be moved to raise the centre of mass by 1 cm?

Answer 1

Let the two masses m₁ and m₂ are kept along a vertical line.

It is given that:
m₁ = 10 kg
m₂ = 30 kg

First block is raised through a height of 7 cm.

Thus, to raise the centre of mass by 1 cm:

$$\begin{gathered} Y\mathrm{cm}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2} \\ \Rightarrow 1=\frac{10\times 7+30\times y_2}{40} \\ \Rightarrow 70+30y_2=40 \\ \Rightarrow 30y_2=-30 \\ \Rightarrow y_2=-1 \end{gathered}$$

Therefore, the 30 kg block (m₂₎ should be moved by 1 cm downwards in order to raise the centre of mass by 1 cm.